Question

A surveyor sights the top of a building with a handheld range finder. the top of the building is 148 feet 2 inches away. the angle of elevation is 56º. find the distance from the surveyor to the building in feet and inches. (sketch and label the situation first.)

Answer 1

To find the distance from the surveyor to the building, we can use trigonometry. By using the tangent function, we can calculate the height of the building and the distance from the surveyor to the building. The distance from the surveyor to the building is approximately 99 feet 6.69 inches.

Step-by-step explanation:

To find the distance from the surveyor to the building, we can use trigonometry. We can use the tangent function to find the opposite side (the height of the building) and the adjacent side (the distance from the surveyor to the building).

Let's convert the distance from feet and inches to inches. 148 feet 2 inches is equal to 148 x 12 + 2 = 1778 inches.

Now we can use the tangent function. tan(56º) = height of the building / distance from the surveyor to the building. Let's call the height of the building 'h' and the distance from the surveyor to the building 'd'. So we have tan(56º) = h / d.

Plugging in the values, we have tan(56º) = h / 1778. To solve for 'd', we can rearrange the equation as d = h / tan(56º).

We can now substitute the known angle and solve for 'd'. d = h / tan(56º) = 1778 / tan(56º) = 1778 / 1.4877 = 1194.69 inches.

Finally, let's convert 'd' back to feet and inches. 1194.69 inches is equal to 1194.69 / 12 = 99 feet 6.69 inches. So, the distance from the surveyor to the building is approximately 99 feet 6.69 inches.

Answer 2

see the attached figure to better understand the problem

we know that

in the right triangle ABC

cos 56°=AC/AB

where

AC is the adjacent side to angle 56 degrees------> the distance from the surveyor to the building

AB is the hypotenuse-----> 148 ft 2 in

56 degrees------> is the angle of elevation

so

cos 56°=AC/AB---------> solve for AC

AC=AB*cos 56°

AB=148 ft 2 in

convert 2 in to ft

1 ft -----> 12 in

x ft------> 2 in

x=2/12-----> x=0.17 ft

AB=148 ft 2 in-----> 148 ft+0.17 ft------> AB=148.17 ft

AC=AB*cos 56°----> AC=148.17*cos 56°------> AC=82.86 ft

convert 0.86 ft to in

0.86 ft=0.86*12-----> 10.32 in

distance AB=82 ft 10 in

the answer is

the distance from the surveyor to the building is 82 ft 10 in